Question

Player A has a $1 bill and a $20 bill, and player B has a $5 bill and a $10 bill. Each player will select a bill from the other player without knowing what bill the other player selected. If the total of the bills is odd, player A gets both of the two bills that were selected, but if the total is even, player B gets both bills.

1. Develop a payoff table for this game. (Place the sum of both bills in each cell.)
2. What are the best strategies for each player?
3. What is the value of the game? Which player would you like to be?

Please be descriptive, thank you!

Answer 1

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(a) Develop a payoff table for this game. (Place the sum of both bills in each cell.)

A       B	$1	$20
$5	0, $6	$25 , 0
$10	$11 , 0	0 , $30

(b) What are the best strategies for each player?

The best strategy for player A is to choose $5 bill when B chooses $20 bill and to choose $10 bill when B chooses $1.

The best strategy for player B is to choose $1 bill when A chooses $5 bill and to choose $20 bill when A chooses $10 bill.

(c) What is the value of the game? Which player would you like to be?

The value of the game is : 1 + 20 + 5 + 10 = $36

This game is not biased against any player. So it does not matter which player you are. If a player is risk averse, he would like to be player A. If the player is risk neutral, he would like to be player B. The above game does not have equilibrium in pure strategies. However, there can be equilibriums in mixed strategies. Depending on the probability that is assigned to each action of each player, we can decide which player will have more benefits.